用半定规划重构量子通道，高效且精度高。
Semidefinite Programming for Quantum Channel Learning
- 将量子通道重建转为半定规划问题，利用凸优化求解。
- 实测表明重构通道的Kraus秩通常不足理论最大值的百分之几。
- 适合量子实验数据处理与量子过程层析研究者使用。
本文研究从经典数据样本中重建量子通道的问题。当总保真度可表示为两个二次型之比时（如混合态映射到纯态、投影算符学习、酉操作学习等），可通过半定规划（SDP）对乔伊矩阵进行保真度优化。由于SDP具有凸性，可被多种数值算法高效求解。我们测试了多个商用SDP求解器，均成功实现了不同形式量子通道的重建。值得注意的是，所得通道的Kraus秩通常远低于其理论最大值（不足百分之几），表明实验观测数据常可用低秩量子通道描述。该理论也被应用于从数据中重构投影算符。最后，我们提出一种基于量子通道变换的经典计算模型，可在经典计算机上实现并可能硬件优化。
原文摘要 · Abstract (English)
The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state, projective operators, unitary learning, and others), Semidefinite Programming (SDP) can be applied to solve the fidelity optimization problem with respect to the Choi matrix. A remarkable feature of SDP is that the optimization is convex, which allows the problem to be efficiently solved by a variety of numerical algorithms. We have tested several commercially available SDP solvers, all of which allowed for the reconstruction of quantum channels of different forms. A notable feature is that the Kraus rank of the obtained quantum channel typically comprises less than a few percent of its maximal possible value. This suggests that a relatively small Kraus rank quantum channel is typically sufficient to describe experimentally observed classical data. The theory was also applied to the problem of reconstructing projective operators from data. Finally, we discuss a classical computational model based on quantum channel transformation, performed and calculated on a classical computer, possibly hardware-optimized.
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